10.6.23 problem 23

Internal problem ID [1240]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 23
Date solved : Monday, January 27, 2025 at 04:47:13 AM
CAS classification : [_linear]

\begin{align*} \left (1+t \right ) y+t y^{\prime }&={\mathrm e}^{2 t} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve((1+t)*y(t)+t*diff(y(t),t) = exp(2*t),y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{2 t}+3 \,{\mathrm e}^{-t} c_1}{3 t} \]

✓ Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 27

DSolve[(1+t)*y[t]+t*D[y[t],t] == Exp[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {e^{2 t}+3 c_1 e^{-t}}{3 t} \]